Exploring crossing times and congestion patterns at scramble intersections in pedestrian dynamics models: A statistical analysis

In this study, we present a model designed to unravel the statistical complexities of pedestrian crossing times and related physical quantities in a unique pedestrian intersection, specifically a double intersecting diagonal crossing. Our model employs an agent-based stochastic process based on a lattice gas dynamics to describe a four-species interaction on an underlying square lattice representing the intersection. This model incorporates four static floor fields guiding each species within the scenario. Our findings emphasize the critical role that the density of highly driven pedestrians plays in the statistics of crossing times by triggering the transition from a normal distribution for low densities to a uniform distribution for a crowded scenario. In the steady state, we mapped the system mobility and showed that an anomalous mobile phase emerges when considering a scenario with high density of poorly driven pedestrians. To monitor these phenomena, we focus on two variables: directed mobility and average distance between agents. We conclude our analysis by overcoming a crucial limitation of the lattice gas model with the introduction of viscosity effects among pedestrians. We observe that mixed state regime emerges as the system presents a mobile-to-immobile phase transition when viscosity effects faints. Our research sheds light on the nuanced dynamics of scramble intersections, contributing to a deeper understanding of urban mobility challenges.